We obtain the queue length probability distribution at equilibrium for a multi-server, single queue with generalised exponential (GE) service time distribution and a Markov modulated compound Poisson arrival process (MMCPP)—i.e. a Poisson point process with bulk arrivals having geometrically distributed batch size whose parameters are modulated by a Markovian arrival phase process. This arrival...

In this paper, we consider a MAP/G/1 queue with MAP arrivals of negative customers, where there are two types of service times and two classes of removal rules: the RCA and RCH, as introduced in Section 2. We provide an approach for analyzing the system. This approach is based on the classical supplementary variable method, combined with the matrix-analytic method and the censoring technique. B...

We consider a queueing system consisting of multiple identical servers and a common queue. The service time follows an exponential distribution and the arrival process is governed by a semi-Markov process (SMP). The motivation to study the queueing system with SMP arrivals lies in that it can model the auto-correlated traffic on the high speed network generated by a real time communication, for...

WiMAX is intended for fourth generation wireless mobile communications where a group of users are provided with a connection and a fixed length queue. In present literature traffic of such network is analyzed based on the generator matrix of the Markov Arrival Process (MAP). In this paper a simple analytical technique of the two dimensional Markov chain is used to obtain the trajectory of the c...

This paper studies the impact of long-range-dependent (LRD) traffic on the performance of reassembly and multiplexing queueing. A queueing model characterizing the general reassembly and multiplexing operations performed in packet networks is developed and analyzed. The buffer overflow probabilities for both reassembly and multiplexing queues are derived by extending renewal analysis and Beneš ...

This paper studies a queueing system with a Markov arrival process and cyclic service times. When customers are distinguished by the types of their service times, the queueing processes experienced by different types of customers are different. First, a computational approach is developed to find the distributions of the queue length and waiting time of each type of customer. The results are us...

In this article we develop a nonparametric Bayesian approach to prediction for the M/G/1 queue, focusing on the imbedded semiMarkov process of the queue at the departure times. Our approach is motivated by queues with a large number of data points and highfrequency systems, where times consuming MCMC/ABC algorithms might be infeasible and a nonparametric approach is desirable to avoid parametri...

Many analytical tools have been devised to analyze CBR video coders, however only few have been applied to the VBR case. In this paper, we present a semi-Markov process model for approximating the stochastic equilibrium queue length distribution for VBR video sources multiplexed onto a constant capacity A TM channel. The sources are assumed to have two rates, and generate cells that pass throug...

We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical MX/G/1 queue with semi-Markov service times is the most prominent example in this class and serves as a vehicle to display our results. The sequence of service times is governed by a modulating process J(t). The state of J(·) at a service initiation t...

Tandem Jackson networks, and more sophisticated variants, have found widespread application in various domains. One such a variant is the tandem queue with server slow-down, in which the server of the upstream queue reduces its service speed as soon as the downstream queue exceeds some prespecified threshold, to provide the downstream queue some sort of ‘protection’. This paper focuses on the o...